Abstract
In Part I a general theory of f f -vectors of simplicial subdivisions (or triangulations) of simplicial complexes is developed, based on the concept of local h h -vector. As an application, we prove that the h h -vector of a Cohen-Macaulay complex increases under “quasi-geometric” subdivision, thus establishing a special case of a conjecture of Kalai and this author. Techniques include commutative algebra, homological algebra, and the intersection homology of toric varieties. In Part II we extend the work of Part I to more general situations. First a formal generalization of subdivision is given based on incidence algebras. Special cases are then developed, in particular one based on subdivisions of Eulerian posets and involving generalized h h -vectors. Other cases deal with Kazhdan-Lusztig polynomials, Ehrhart polynomials, and a q q -analogue of Eulerian posets. Many applications and examples are given throughout.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.